Necessary and sufficient conditions for the convergence of \(\text{Orthomin}(k)\) on singular and inconsistent linear systems

DOI10.1007/s002110000185zbMath0966.65033OpenAlexW2068335126MaRDI QIDQ1592354

Yoshio Oyanagi, Masaaki Sugihara, Shao-Liang Zhang

Publication date: 1 August 2001

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002110000185

zbMATH Keywords

convergence numerical examples Poisson's equation iterative method conjugate gradient method criteria for breakdown Orthomin\((k)\) method singular and inconsistent linear systems

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (13)

A two-step iterative method and its acceleration for outer inverses ⋮ A geometric view of Krylov subspace methods on singular systems ⋮ A variant algorithm of the Orthomin\((m)\) method for solving linear systems ⋮ An iterative method for solving singular linear systems with index one ⋮ A family of iterative methods with accelerated convergence for restricted linear system of equations ⋮ Semistability of Steepest Descent with Momentum for Quadratic Functions ⋮ A generalized preconditioned HSS method for singular saddle point problems ⋮ Solving EP singular linear systems ⋮ On the semi-convergence of regularized HSS iteration methods for singular saddle point problems ⋮ Convergence and quotient convergence of iterative methods for solving singular linear equations with index one ⋮ On the convergence of general stationary iterative methods for range-Hermitian singular linear systems ⋮ Convergence ofP-regular splitting iterative methods for non-Hermitian positive semidefinite linear systems ⋮ A note on solving EP inconsistent linear systems

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